I. U. Bronshtein's Conjecture for Monotone Nonautonomous Dynamical Systems

TL;DR

This paper proves Bronshtein's conjecture, showing that solutions of certain dissipative, monotone almost periodic differential and difference equations are themselves almost periodic, advancing understanding of their long-term behavior.

Contribution

It provides a positive resolution to Bronshtein's conjecture specifically for monotone almost periodic systems, a case previously unresolved.

Findings

Solutions are almost periodic under the given conditions.

The conjecture holds for both differential and difference equations.

Advances the theory of almost periodic solutions in dissipative systems.

Abstract

In this paper we study the problem of almost periodicity of solutions for dissipative differential equations (Bronshtein's conjecture). We give a positive answer to this conjecture for monotone almost periodic systems of differential/difference equations.